Problem: Express your answer as a mixed number simplified to lowest terms. $8\dfrac{2}{3}-5\dfrac{7}{8} = {?}$
Find a common denominator for the fractions: $= {8\dfrac{16}{24}}-{5\dfrac{21}{24}}$ Convert ${8\dfrac{16}{24}}$ to ${7 + \dfrac{24}{24} + \dfrac{16}{24}}$ So the problem becomes: ${7\dfrac{40}{24}}-{5\dfrac{21}{24}}$ Separate the whole numbers from the fractional parts: $= {7} + {\dfrac{40}{24}} - {5} - {\dfrac{21}{24}}$ Bring the whole numbers together and the fractions together: $= {7} - {5} + {\dfrac{40}{24}} - {\dfrac{21}{24}}$ Subtract the whole numbers: $=2 + {\dfrac{40}{24}} - {\dfrac{21}{24}}$ Subtract the fractions: $= 2+\dfrac{19}{24}$ Combine the whole and fractional parts into a mixed number: $= 2\dfrac{19}{24}$